Pub Date : 2024-09-01DOI: 10.1134/s096554252470074x
J. Cummings, M. Hamilton, T. Kieu
Abstract
In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow of a single-phase fluid in ({{mathbb{R}}^{d}},;d geqslant 2) by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stabilit1y of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.
{"title":"A Mixed Finite Element Approximation for Fluid Flows of Mixed Regimes in Porous Media","authors":"J. Cummings, M. Hamilton, T. Kieu","doi":"10.1134/s096554252470074x","DOIUrl":"https://doi.org/10.1134/s096554252470074x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow of a single-phase fluid in <span>({{mathbb{R}}^{d}},;d geqslant 2)</span> by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stabilit1y of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700672
A. M. Voloshchenko
Abstract
For the transport equation in three-dimensional (r,;vartheta ,;z) geometry, a (K{{P}_{1}})-scheme is constructed for accelerating the convergence of upscatter iterations over the neutron thermalization region and the fission source in solving a subcritical boundary value problem, consistent with the Weighted Diamond Differencing (WDD) scheme, and its generalization to the case of nodal Linear Discontinues (LD) and Linear Best (LB) schemes of the 3rd and 4th order of accuracy in spatial variables is considered. To solve the system for accelerating corrections, an algorithm based on the use of the cyclic splitting method was used, similar to that used earlier when constructing the (K{{P}_{1}})-scheme for accelerating the convergence of inner iterations. An algorithm for determining the energy dependence for accelerating corrections of the (K{{P}_{1}})-scheme for accelerating the convergence of upscatter iterations is considered. The choice of a criterion for the convergence of upscatter iterations is considered, and a criterion integral over up-scattered thermal neutrons for the convergence of upscatter iterations over the region of neutron thermalization is proposed. A modification of the algorithm for the case of three-dimensional (x,;y,;z) geometry is considered. Numerical examples of using the (K{{P}_{1}})-scheme for accelerating the convergence of upscatter iterations to solve typical problems of neutron transport in three-dimensional geometry are given.
AbstractFor the transport equation in three-dimensional (r,;vartheta ,. z) geometry；z)几何中的输运方程，构建了一种与加权菱形微分（WDD）方案相一致的用于加速中子热化区和裂变源上散射迭代收敛的（K{{P}_{1}}）方案，并考虑了将其推广到空间变量精度为3阶和4阶的节点线性不连续（LD）和线性最佳（LB）方案的情况。为了求解加速修正系统，使用了一种基于循环分裂法的算法，类似于之前构建 (K{{P}_{1}}) 方案以加速内部迭代收敛时使用的算法。研究考虑了一种算法，用于确定加速上散射迭代收敛的(K{{P}_{1}})方案加速修正的能量依赖性。考虑了上散射迭代收敛标准的选择，并提出了中子热化区域上散射热中子迭代收敛的标准积分。考虑了针对三维 (x,;y,;z) 几何形状的算法修改。给出了使用 (K{{P}_{1}}) 方案加速上散射迭代收敛以解决三维几何中子输运典型问题的数值示例。
{"title":"KP1-Scheme for Acceleration of Upscatter Iterations over the Neutron Thermalization Region and the Fission Source in Solving a Subcritical Boundary Value Problem","authors":"A. M. Voloshchenko","doi":"10.1134/s0965542524700672","DOIUrl":"https://doi.org/10.1134/s0965542524700672","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>For the transport equation in three-dimensional <span>(r,;vartheta ,;z)</span> geometry, a <span>(K{{P}_{1}})</span>-scheme is constructed for accelerating the convergence of upscatter iterations over the neutron thermalization region and the fission source in solving a subcritical boundary value problem, consistent with the Weighted Diamond Differencing (WDD) scheme, and its generalization to the case of nodal Linear Discontinues (LD) and Linear Best (LB) schemes of the 3rd and 4th order of accuracy in spatial variables is considered. To solve the system for accelerating corrections, an algorithm based on the use of the cyclic splitting method was used, similar to that used earlier when constructing the <span>(K{{P}_{1}})</span>-scheme for accelerating the convergence of inner iterations. An algorithm for determining the energy dependence for accelerating corrections of the <span>(K{{P}_{1}})</span>-scheme for accelerating the convergence of upscatter iterations is considered. The choice of a criterion for the convergence of upscatter iterations is considered, and a criterion integral over up-scattered thermal neutrons for the convergence of upscatter iterations over the region of neutron thermalization is proposed. A modification of the algorithm for the case of three-dimensional <span>(x,;y,;z)</span> geometry is considered. Numerical examples of using the <span>(K{{P}_{1}})</span>-scheme for accelerating the convergence of upscatter iterations to solve typical problems of neutron transport in three-dimensional geometry are given.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700763
Zhiqiang Sun, Guolin Hou, Yanfen Qiao, Jincun Liu
Abstract
A Hamiltonian system is developed for the three-dimensional (3D) problem of two-dimensional (2D) decagonal piezoelectric quasicrystals via the variational principle. Based on the full state vector and the properties of the Hamiltonian operator matrix, the superposition principle of solutions obtains the symplectic analytical solutions of the problem under simply supported boundary conditions. Numerical examples are illustrated to display the effects of the stacking sequences and material constants on the stresses, displacements, electric potential, and electric displacements under the mechanical and electric displacement loadings. The symplectic analytical solutions presented in the article can be used as a reference for further numerical research.
{"title":"Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions","authors":"Zhiqiang Sun, Guolin Hou, Yanfen Qiao, Jincun Liu","doi":"10.1134/s0965542524700763","DOIUrl":"https://doi.org/10.1134/s0965542524700763","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A Hamiltonian system is developed for the three-dimensional (3D) problem of two-dimensional (2D) decagonal piezoelectric quasicrystals via the variational principle. Based on the full state vector and the properties of the Hamiltonian operator matrix, the superposition principle of solutions obtains the symplectic analytical solutions of the problem under simply supported boundary conditions. Numerical examples are illustrated to display the effects of the stacking sequences and material constants on the stresses, displacements, electric potential, and electric displacements under the mechanical and electric displacement loadings. The symplectic analytical solutions presented in the article can be used as a reference for further numerical research.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700696
I. E. Stepanova, I. I. Kolotov, A. G. Yagola, A. N. Levashov
Abstract
The paper examines the problem of unique determination of the fundamental solution of a mesh analogue of Laplace’s equation within the theory of discrete gravitational potential. The mesh fundamental solution of the finite-difference analogue of Laplace’s equation plays a key role in reconstructing a continuously distributed source of gravitational or magnetic field from heterogeneous and different-precision data obtained at points of a certain mesh set.
{"title":"On the Uniqueness of Determining the Mesh Fundamental Solution of Laplace’s Equation in the Theory of Discrete Potential","authors":"I. E. Stepanova, I. I. Kolotov, A. G. Yagola, A. N. Levashov","doi":"10.1134/s0965542524700696","DOIUrl":"https://doi.org/10.1134/s0965542524700696","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper examines the problem of unique determination of the fundamental solution of a mesh analogue of Laplace’s equation within the theory of discrete gravitational potential. The mesh fundamental solution of the finite-difference analogue of Laplace’s equation plays a key role in reconstructing a continuously distributed source of gravitational or magnetic field from heterogeneous and different-precision data obtained at points of a certain mesh set.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700647
M. O. Korpusov, R. S. Shafir, A. K. Matveeva
Abstract
A system of equations with nonlinearity in the electric field potential and temperature is proposed for describing the heating of semiconductor elements on an electrical board with thermal and electrical breakdowns possibly arising over time. A method for numerical diagnostics of solution blow-up is considered. In the numerical analysis of the problem, the original system of partial differential equations is reduced to a differential-algebraic system, which is solved using a single-stage Rosenbrock scheme with complex coefficients. The blow-up of the exact solution is detected using an asymptotically sharp a posteriori error estimate obtained by computing approximate solutions on sequentially refined grids. The blow-up time is numerically estimated in the case of various initial conditions.
{"title":"Numerical Diagnostics of Solution Blow-Up in a Thermoelectric Semiconductor Model","authors":"M. O. Korpusov, R. S. Shafir, A. K. Matveeva","doi":"10.1134/s0965542524700647","DOIUrl":"https://doi.org/10.1134/s0965542524700647","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A system of equations with nonlinearity in the electric field potential and temperature is proposed for describing the heating of semiconductor elements on an electrical board with thermal and electrical breakdowns possibly arising over time. A method for numerical diagnostics of solution blow-up is considered. In the numerical analysis of the problem, the original system of partial differential equations is reduced to a differential-algebraic system, which is solved using a single-stage Rosenbrock scheme with complex coefficients. The blow-up of the exact solution is detected using an asymptotically sharp a posteriori error estimate obtained by computing approximate solutions on sequentially refined grids. The blow-up time is numerically estimated in the case of various initial conditions.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700623
D. Yu. Ivanov
Abstract
Semi-analytical approximations to the tangential derivative (TD) and normal derivative (ND) of the single-layer potential (SLP) near the boundary of a two-dimensional domain, within the framework of the collocation boundary element method and not requiring approximation of the coordinate functions of the boundary, are proposed. To obtain approximations, analytical integration over the smooth component of the distance function and a special additive-multiplicative method for separation of singularities are used. It is proved that such approximations have a more uniform convergence near the domain boundary compared to similar approximations of the TD and ND of SLP based on a simple multiplicative method of separation of singularities. One of the reasons for the highly nonuniform convergence of traditional approximations to TD and ND of SLP based on the Gaussian quadrature formulas is established.
{"title":"On the Uniform Convergence of Approximations to the Tangential and Normal Derivatives of the Single-Layer Potential Near the Boundary of a Two-Dimensional Domain","authors":"D. Yu. Ivanov","doi":"10.1134/s0965542524700623","DOIUrl":"https://doi.org/10.1134/s0965542524700623","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Semi-analytical approximations to the tangential derivative (TD) and normal derivative (ND) of the single-layer potential (SLP) near the boundary of a two-dimensional domain, within the framework of the collocation boundary element method and not requiring approximation of the coordinate functions of the boundary, are proposed. To obtain approximations, analytical integration over the smooth component of the distance function and a special additive-multiplicative method for separation of singularities are used. It is proved that such approximations have a more uniform convergence near the domain boundary compared to similar approximations of the TD and ND of SLP based on a simple multiplicative method of separation of singularities. One of the reasons for the highly nonuniform convergence of traditional approximations to TD and ND of SLP based on the Gaussian quadrature formulas is established.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700660
A. A. Belov, Zh. O. Dombrovskaya
Abstract
In recent years, much attention has been paid to integrated photonics devices based on nonlinear media. A generalization of the transfer matrix method to problems in plane-parallel layered media with quadratic and cubic nonlinearity is proposed. The incident radiation can be either a monochromatic wave or a non-monochromatic pulse. Previously, such problems could only be solved using grid methods. The proposed approaches significantly expand the range of applicability of matrix methods and are drastically superior in efficiency to the well-known grid methods.
{"title":"Generalization of the Method of Scattering Matrices to Problems in Nonlinear Dispersion Media","authors":"A. A. Belov, Zh. O. Dombrovskaya","doi":"10.1134/s0965542524700660","DOIUrl":"https://doi.org/10.1134/s0965542524700660","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In recent years, much attention has been paid to integrated photonics devices based on nonlinear media. A generalization of the transfer matrix method to problems in plane-parallel layered media with quadratic and cubic nonlinearity is proposed. The incident radiation can be either a monochromatic wave or a non-monochromatic pulse. Previously, such problems could only be solved using grid methods. The proposed approaches significantly expand the range of applicability of matrix methods and are drastically superior in efficiency to the well-known grid methods.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700684
V. N. Malozemov, N. A. Solov’eva, G. Sh. Tamasyan
Abstract
When developing numerical methods for solving nonlinear minimax problems, the following auxiliary problem arose: in the convex hull of a certain finite set in Euclidean space, find a point that has the smallest norm. In 1971, B. Mitchell, V. Demyanov and V. Malozemov proposed a non-standard algorithm for solving this problem, which was later called the MDM algorithm (based on the first letters of the authors' last names). This article considers a specific minimax problem: finding the smallest volume ball containing a given finite set of points. It is called the Sylvester problem and is a special case of the problem about the Chebyshev center of a set. The Sylvester problem is associated with a convex quadratic programming problem with simplex constraints. To solve this problem, it is proposed to use a variant of the MDM algorithm. With its help, a minimizing sequence of feasible solutions is constructed such that two consecutive feasible solutions differ in only two components. The indices of these components are selected based on certain optimality conditions. We prove the weak convergence of the resulting sequence of feasible solutions that implies that the corresponding sequence of vectors converges in norm to a unique solution to the Sylvester problem. Four typical examples on a plane are given.
{"title":"The MDM Algorithm and the Sylvester Problem","authors":"V. N. Malozemov, N. A. Solov’eva, G. Sh. Tamasyan","doi":"10.1134/s0965542524700684","DOIUrl":"https://doi.org/10.1134/s0965542524700684","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>When developing numerical methods for solving nonlinear minimax problems, the following auxiliary problem arose: in the convex hull of a certain finite set in Euclidean space, find a point that has the smallest norm. In 1971, B. Mitchell, V. Demyanov and V. Malozemov proposed a non-standard algorithm for solving this problem, which was later called the MDM algorithm (based on the first letters of the authors' last names). This article considers a specific minimax problem: finding the smallest volume ball containing a given finite set of points. It is called the Sylvester problem and is a special case of the problem about the Chebyshev center of a set. The Sylvester problem is associated with a convex quadratic programming problem with simplex constraints. To solve this problem, it is proposed to use a variant of the MDM algorithm. With its help, a minimizing sequence of feasible solutions is constructed such that two consecutive feasible solutions differ in only two components. The indices of these components are selected based on certain optimality conditions. We prove the weak convergence of the resulting sequence of feasible solutions that implies that the corresponding sequence of vectors converges in norm to a unique solution to the Sylvester problem. Four typical examples on a plane are given.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s096554252470060x
A. G. Vikulov
Abstract
Thermodynamic calculation of a cycle in a two-phase region requires an equation of state of the working medium, which is used as a virial equation with unknown temperature functions. A degenerate system of algebraic equations has been constructed for unknown coefficients, which are the values of virial functions on a temperature mesh. Based on the regularization method, a variational-iterative algorithm for solving a degenerate system of equations has been developed. A computational experiment to confirm the effectiveness of the method was carried out.
{"title":"Regularization of the Solution to Degenerate Systems of Algebraic Equations Exemplified by Identification of the Virial Equation of State of a Real Gas","authors":"A. G. Vikulov","doi":"10.1134/s096554252470060x","DOIUrl":"https://doi.org/10.1134/s096554252470060x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Thermodynamic calculation of a cycle in a two-phase region requires an equation of state of the working medium, which is used as a virial equation with unknown temperature functions. A degenerate system of algebraic equations has been constructed for unknown coefficients, which are the values of virial functions on a temperature mesh. Based on the regularization method, a variational-iterative algorithm for solving a degenerate system of equations has been developed. A computational experiment to confirm the effectiveness of the method was carried out.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700702
A. D. Chernyshov, O. Yu. Nikiforova, V. V. Goryainov, I. G. Rukin
Abstract
The foundations of fast universal trigonometric interpolation for nonperiodic functions used to obtain high-accuracy approximate solutions are described. High-accuracy formulas are derived for computing the launch point coordinates of a flight vehicle by applying universal fast trigonometric interpolation combined with extrapolation at the endpoints of a given interval. Numerical experiments show that, after launching the first vehicle, the launch point coordinates can be determined in 7 s with accuracy of ({{10}^{{ - 17}}}) m.
{"title":"Application of Universal Fast Trigonometric Interpolation and Extrapolation for Determining the Launch Point Coordinates of a Flight Vehicle","authors":"A. D. Chernyshov, O. Yu. Nikiforova, V. V. Goryainov, I. G. Rukin","doi":"10.1134/s0965542524700702","DOIUrl":"https://doi.org/10.1134/s0965542524700702","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The foundations of fast universal trigonometric interpolation for nonperiodic functions used to obtain high-accuracy approximate solutions are described. High-accuracy formulas are derived for computing the launch point coordinates of a flight vehicle by applying universal fast trigonometric interpolation combined with extrapolation at the endpoints of a given interval. Numerical experiments show that, after launching the first vehicle, the launch point coordinates can be determined in 7 s with accuracy of <span>({{10}^{{ - 17}}})</span> m.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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